The theory of ultrasonic wave propagation in textured polycrystals presented previously [S. Hirsekorn, J. Acoust. Soc. Am.77, 832–843 (1985)] for propagation and polarization parallel to symmetry axes of texture is generalized to calculate the directional‐dependent scattering coefficients and phase and group velocities of plane waves with arbitrary propagation and polarization direction as a function of frequency. The analytical calculations are carried out for cubic polycrystals with orthorhombic texture symmetry. Numerical evaluation is done for an austenitic weld metal. The results are compared to those of the frequency‐independent description of ultrasonic propagation.